Drilling fluid, also known as “drilling mud” or “mud,” has been employed in drilling for a many years. Drilling fluids may be water based, oil based or synthetic based. Any of a number of liquid and gaseous fluids and mixtures of fluids and solids (as solid suspensions, mixtures and emulsions of liquids, gases and solids) used in operations to drill boreholes into the earth may be used as drilling fluids. In addition, drilling fluids may contain emulsified water, oil, suspended solids or a combination of these materials. In short, drilling fluids may be any substance that will limit or prevent formation fluids from entering a wellbore.
Among the positive benefits of drilling mud is better control of the wellbore. Specifically, if the drilling fluid is of an appropriate weight it can, at least in part, assist in controlling unwanted inflow into the wellbore from the surrounding formation. The weight of the drilling fluid can also help prevent the collapse of the borehole or casing. Broadly speaking, because the specific gravity of the drilling fluid is greater than the specific gravity of the surrounding fluids in the wellbore, formation fluids are largely prevented from entering the wellbore.
Because the drilling fluid is under pressure, it may “cake” on the borehole wall. When drilling fluid adheres to the borehole wall, it is commonly referred to as “mudcake.” From the perspective of a driller, mudcake may have both positive and negative aspects. A certain level of mudcake build up is desirable to isolate the formation fluid from the wellbore.
On the other hand, mud may penetrate into the formation surrounding the wellbore. If excessive mudcake deposition occurs, issues such as stuck pipe and damage to the formation may occur. In addition, if mudcake thickness is inappropriately excessive, it may be more difficult for formation fluids, such as oil and gas, to be extracted from the formation. As such, it is desirable to know if mudcake is present in the borehole and also the thickness of the mudcake in the wellbore.
Currently, several tools are sensitive to the presence and thickness of mudcake. Among these tools are a microlog tool, a microlaterolog tool and an electric image logging tool.
A prior art microlog tool E is illustrated in FIGS. 1A and 1B. Microlog or microelectrolog devices or tools, as their names imply, are electrical logging tools with electrodes. The electrodes are mounted on pads which are kept in contact with the wellbore, also known as a borehole, wall. The microlog tool seen in FIGS. 1A and 1B utilizes an unfocused measurement based on the principle of a normal and a lateral.
In operation, current is emitted from a button Ao, and the potentials of the two electrodes M1 and M2 are measured. To ensure a shallow depth of investigation, the spacing between electrodes M1 and M2 is on the order of about one inch. The difference in the potential between electrodes M1 and M2 forms a lateral or inverse measurement that is mostly influenced by the presence of mudcake on the adjacent borehole wall.
The potential on electrode M2 forms a normal measurement which, being farther from the current source, is influenced more by the flushed zone. The influence of mudcake, especially in the case of resistive formation and a conductive and thick mudcake, is a major disadvantage for the purpose of determining Rxo. (flushed zone resistivity). However, the electromagnetic curves separated when there is an invasion of the formation by the mud. This separation has proven to be a reliable indicator of permeable zones. In other words, because the mud is able to enter the formation, the formation is likely sufficiently permeable to allow hydrocarbons to flow into the borehole and, ultimately, to the surface for extraction and sale.
In order to improve the determination of Rxo, (flushed zone resistivity), a focused or microlaterolog device L was developed. As illustrated in FIGS. 2A and 2B, the microlaterolog device L employs a bucking current from electrode A1 which focuses the measurement current to penetrate the mudcake. Depending on the contrast between Rxo and Rt (True Formation Resistivity), 90% of the measured signal comes from the first two to four inches in front of the pad, i.e. where mudcake is located in the borehole.
A borehole electrical image logging tool is an important logging tool and, at the present time, has the highest resolution of any presently existing electrical logging tool that is sensitive to presence of mudcake. Examples of such tools are the FMI, STAR-II, EMI and CMI. These tools are produced by Schlumberger, Baker Hughes, Halliburton and Weatherford, respectively. A typical borehole electrical image logging tool B is illustrated in FIGS. 3A, 3B and 3C. As illustrated in FIG. 3A, tool B has six arms 45 equally disposed about a mandrel 55 with a 60 degree azimuth interval. As illustrated in FIGS. 3A and 3B, each arm 45 has a metal pad 65. The pad 65 illustrated in FIGS. 3B and 3C have 12 buttons 85 located on each pad 65 and arranged in two rows. As an example, in tool B, the vertical distance between the two rows is 0.76 cm and the horizontal shift is 0.25 cm. The diameter of the buttons 85 is 0.41 cm, and the outer diameter of the insulating ring of the buttons is 0.61 cm. The six pads 65 fix on the bottom of mandrel 55 and the current return electrode 95 is put on the top of the mandrel 55. It is also desirable to have an insulator disposed between current return electrode 95 and pad 14. As a non-limiting example, current return electrode can be located on mandrel 55.
During measurement, the pads 65 and buttons 85 are kept at a substantially equal potential and the current of each button 85 is measured. Next, the resistance from button 85 to return electrode 95 is calculated from the potential difference between the pad 65 and the return electrode 95 and the current of the button 85. The electrical image of the borehole will be obtained by converting these resistances to grey value and putting together according to their position.
It is known from the 2008 paper entitled “Full 3-D numerical modeling of borehole electric image logging and evaluation model of fracture” that a borehole image from an electrical imager is a popular deliverable in well logging.
As taught in Ke ShiZhen, the response of a borehole imager can be mathematically modeled as follows:
According to the principle and technical specification of a borehole electric image logging tool, the scalar potential in formation u(x,y,z) satisfies the following calculus variations:
                                          F            ⁡                          (              u              )                                =                                                                      1                  2                                ⁢                                                      ∫                                          ∫                      ∫                                                        Ω                                ⁢                                  σ                  ⁡                                      [                                                                                            (                                                                                    ∂                              u                                                                                      ∂                              x                                                                                )                                                2                                            +                                                                        (                                                                                    ∂                              u                                                                                      ∂                              y                                                                                )                                                2                                            +                                                                        (                                                                                    ∂                              u                                                                                      ∂                              z                                                                                )                                                2                                                              ]                                                  ⁢                                  ⅆ                  x                                ⁢                                  ⅆ                  y                                ⁢                                  ⅆ                  z                                            -                                                ∑                  E                                ⁢                                                      I                    E                                    ⁢                                      U                    E                                                                        ->            min                          ,                            (        1        )            
where σ is the conductivity of media, IE is the current of button, UE is the potential of the button, F(u) is the function of potential.
By scattering, the element stiffness can be calculated using the following formula:
                                          K            ij            e                    =                                                    ∫                                  ∫                  ∫                                            e                        ⁢                          σ              ⁡                              [                                                                                                    ∂                                                  N                          i                                                                                            ∂                        x                                                              ⁢                                                                  ∂                                                  N                          j                                                                                            ∂                        x                                                                              +                                                                                    ∂                                                  N                          i                                                                                            ∂                        y                                                              ⁢                                                                  ∂                                                  N                          j                                                                                            ∂                        y                                                                              +                                                                                    ∂                                                  N                          i                                                                                            ∂                        z                                                              ⁢                                                                  ∂                                                  N                          j                                                                                            ∂                        z                                                                                            ]                                      ⁢                          ⅆ              x                        ⁢                          ⅆ              y                        ⁢                          ⅆ              z                                      ,                            (        2        )            
where Ni, Nj are shape function.
The conductivity distribution of the model is as follows:
  σ  =      {                                                      σ              m                        ,                                                in            ⁢                                                  ⁢            borehole                                                                          σ              t                        ,                                                outside            ⁢                                                  ⁢            borehole                              
where σm is the conductivity of mud and σt is the conductivity of the formation.
It is also taught by Ke ShiZhen that the potential of the pads and buttons are kept substantially equal and set to 10 volts in that particular work.